
The present ages of Ramesh and his elder brother are in the ratio 5:7. After 5 years, the ratio of their ages will be 3:4. Find their present ages?
Answer
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Hint: The present ages of Ramesh and his elder brother are in the ratio 5:7 so converting the ratio to number by multiplying each number in the ratio by x so the present age of Ramesh becomes 5x and his elder brother is 7x. Now, after 5 years, the age of Ramesh and his elder brother is the addition of 5 in their ages before 5 years. Now, take the ratio of the ages of Ramesh and his elder brother and equate it to $\dfrac{3}{4}$. In this way, we will get the value of x and hence their present ages.
Complete step by step solution:
The present ages of Ramesh and his elder brother are given in the following ratio:
5:7
Now, converting the above ratio to number by multiplying each number in the ratio to x and we get,
$5x,7x$
From the above, the present ages of Ramesh and his elder brother is $5x\And 7x$ respectively.
After 5 years, the age of Ramesh and his elder brother respectively is as follows:
$\begin{align}
& 5x+5; \\
& 7x+5 \\
\end{align}$
Now, taking the ratio of the above ages and equating the above ratio to 3:4 we get,
$\Rightarrow \dfrac{5x+5}{7x+5}=\dfrac{3}{4}$
Cross multiplying the above equation we get,
$\begin{align}
& \Rightarrow 4\left( 5x+5 \right)=3\left( 7x+5 \right) \\
& \Rightarrow 20x+20=21x+15 \\
\end{align}$
Rearranging the above equation in such a way so that x terms on one side of the equation and the constant terms on another side of the equation.
$\begin{align}
& \Rightarrow 21x-20x=20-15 \\
& \Rightarrow x=5 \\
\end{align}$
Now, substituting the above value of x in $5x,7x$ we get,
$\begin{align}
& \Rightarrow 5\left( 5 \right),7\left( 5 \right) \\
& =25,35 \\
\end{align}$
Hence, the present age of Ramesh is 25 years and the present age of his elder brother is 35 years.
Note: Always remember that age of a person is not defined in decimals so if you are getting the age of a person in decimal points then it means you have made some mistake. So, this is one of the methods through which you can check the age of the individuals.
Complete step by step solution:
The present ages of Ramesh and his elder brother are given in the following ratio:
5:7
Now, converting the above ratio to number by multiplying each number in the ratio to x and we get,
$5x,7x$
From the above, the present ages of Ramesh and his elder brother is $5x\And 7x$ respectively.
After 5 years, the age of Ramesh and his elder brother respectively is as follows:
$\begin{align}
& 5x+5; \\
& 7x+5 \\
\end{align}$
Now, taking the ratio of the above ages and equating the above ratio to 3:4 we get,
$\Rightarrow \dfrac{5x+5}{7x+5}=\dfrac{3}{4}$
Cross multiplying the above equation we get,
$\begin{align}
& \Rightarrow 4\left( 5x+5 \right)=3\left( 7x+5 \right) \\
& \Rightarrow 20x+20=21x+15 \\
\end{align}$
Rearranging the above equation in such a way so that x terms on one side of the equation and the constant terms on another side of the equation.
$\begin{align}
& \Rightarrow 21x-20x=20-15 \\
& \Rightarrow x=5 \\
\end{align}$
Now, substituting the above value of x in $5x,7x$ we get,
$\begin{align}
& \Rightarrow 5\left( 5 \right),7\left( 5 \right) \\
& =25,35 \\
\end{align}$
Hence, the present age of Ramesh is 25 years and the present age of his elder brother is 35 years.
Note: Always remember that age of a person is not defined in decimals so if you are getting the age of a person in decimal points then it means you have made some mistake. So, this is one of the methods through which you can check the age of the individuals.
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